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  • Open Access

Modulation of high-energy electrons with a nanopore matter lens

Guangyi Huang*, Wenhao He*, Xian Li, and Changlin Zheng†

  • State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China

  • *These authors contributed equally to this work.
  • †Contact author: zcl@fudan.edu.cn
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Phys. Rev. Research 8, 023345 – Published 26 June, 2026

DOI: https://doi.org/10.1103/2mgp-xgv1

Abstract

We demonstrate the modulation of high-energy electrons using a nanosized pore in solid as a strong electrostatic lens. The inner Coulomb potential of matter decreases rapidly from the edge of the pore toward the center, creating a strong electric field on the order of 10 GV/m. This electric field strongly modulates the phase of the incident electron beam and deflects the beam as a defocusing lens. We measure the strength of the electric field by combining electron holography with quantitative scanning transmission electron microscopy. We also observe changes in the transmitted probe through the nanopore using electron confocal imaging. The shrinking electron Airy patterns on the detector plane indicate that the exit probe's convergent angle increases under the deflection of the nanolens. This behavior corresponds to an effective concave lensing effect that cannot be achieved with rotationally symmetric electromagnetic fields in vacuum due to fundamental constraints imposed by the governing field equation. This demonstration of electron matter lensing shows the potential to manipulate high-energy electrons at the nanometer scale, expanding conventional electromagnetic lensing into nanoelectron optics.

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Phys. Rev. Research 8, 023345– Published 26 June, 2026
  • Received 31 December 2023
  • Accepted 3 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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